Hello

Find $\displaystyle a_n$ and $\displaystyle b_n$ such that:

{$\displaystyle an$} , {$\displaystyle b_n$} are divergent sequences

$\displaystyle a_n,b_n > 0$ for $\displaystyle n\geq1$

and { $\displaystyle a_n+b_n$ } is a convergent sequences.

The problem here is both must positive.

If not, $\displaystyle a_n=n$ and $\displaystyle b_n=-n$ is a nice counter-example.

But they must be positive.